Reference no: EM132318402

Question 1:

Lottery: I buy one of 250 raffle tickets for $10. The sponsors then randomly select 1 grand prize worth $200, 2 second prizes worth $100 each, and 3 third prizes worth $50 each. Below is the discrete probability distribution for this raffle.

Prize	P(x)
Grand	1/250
Second	2/250
Third	3/250
None	244/250

(a) Recognizing that I spent $10 to buy a ticket, determine the expected value of this raffle to me as a player. Round your answer to the nearest penny.

(b) What is an accurate interpretation of this value?

It represents how much you would lose every time you play the game. It represents how much you would win every time you play the game. It represents the per-game average you would win/lose if you were to play this game many many times. It is meaningless because you can't actually win or lose this amount.

(c) Based on your answers, would this raffle be a good financial investment for you and why? There is only one correct answer and reason.
Yes, because the expected value is positive. Yes, because the expected value is negative. No, because the expected value is positive. No, because the expected value is negative.

Question 2:

Lottery: I buy one of 400 raffle tickets for $10. The sponsors then randomly select 1 grand prize worth $800, then 2 second prizes worth $200 each, and then 10 third prizes worth $50 each. The selections are made without replacement.

(a) Complete the probability distribution for this raffle. Give your probabilities as a decimal (rounded to 4 decimal places) or as a fraction.

Outcomes                      P(x)

Win Grand Prize

Win a Second Prize

Win a Third Prize

Win Nothing

(b) Recognizing that I spent $10 to buy a ticket, determine the expected value of this raffle to me as a player. Round your answer to the nearest penny.

(c) What is an accurate interpretation of this value?

It represents how much you would win every time you play the game. It represents the per-game average you would win/lose if you were to play this game many many times. It represents how much you would lose every time you play the game. It is meaningless because you can't actually win or lose this amount.

Question 3:

Warranty: You buy a cell phone for $95 and there is a8% chance that it will fail. You can pay an additional $6 for the hassle-free replacement warranty. This means if it fails you will get a free replacement.

(a) Suppose you do not buy the warranty but will buy a second one if the first one fails (we will assume this second one does not fail) and you will pay the full $95 for the second one. Complete the following table to assist in calculating the expected cost for this phone. Enter the probabilities to 2 decimal places.

Outcomes cost = x Probability = P(x)
It fails

It doesn't fail

(b) Use the table to calculate the expected value for the cost of this phone. Round your answer to the nearest penny.

(c) Considering the expected cost above and the price of the warranty ($6), did you make the right decision to not buy the warranty and why? There is only one correct answer and explanation.

Yes, because the expected cost is less than the cost of the phone plus the warranty. No, because the expected cost is greater than the cost of the phone plus the warranty. Yes, because the expected cost is greater than the cost of the phone plus the warranty. No, because the expected cost is less than the cost of the phone plus the warranty.

Question 4:

Life Insurance: Your company sells life insurance. You charge a 55 year old man $75 for a one year, $100,000 policy. If he dies over the course of the next year you pay out $100,000. If he lives, you keep the $75. Based on historical data (relative frequency approximation) the average 55 year old man has a 0.9998 probability of living another year.

(a) What is your expected profit on this policy?

(b) What is an accurate interpretation of this value?

It represents the loss on every policy sold. It is meaningless because the insurance company never makes this amount on a policy. It represents the average profit per policy sold that you would expect if you sold a lot of these policies. It represents the profit on every policy sold.

Calculate the following binomial probability by either using one of the binomial probability tables, software, or a calculator using the formula below. Round your answer to 3 decimal places.

P(x | n, p) =
n!
(n - x)! x!
•p^x•qⁿ - x where q = 1 - p
P(x<14, n = 15, p = 0.8)
=

Calculate the following binomial probability by either using one of the binomial probability tables, software, or a calculator using the formula below. Round your answer to 3 decimal places.
P(x | n, p) =
n!
(n - x)! x!
•p^x•q^{n - x} where q = 1 - p
P(x = 6, n = 10, p = 0.3)
=

Calculate the following binomial probability by either using one of the binomial probability tables, software, or a calculator using the formula below. Round your answer to 3 decimal places.
P(x | n, p ) =
n!
(n - x)! x!
•p^x•q^{n - x} where q = 1 - p
P(x<4, n = 10, p = 0.4) =

Calculate the following binomial probability by either using one of the binomial probability tables, software, or a calculator using the formula below. Round your answer to 3 decimal places.
P(x | n, p) =
n!
(n - x)! x!
•p^x•q^{n - x} where q = 1 - p
P(x = 12, n = 14, p = 0.80) =

Question 5:

T/F Quiz: Suppose you take a 15 question True or False quiz and you guess on every problem. You only get 4 correct.

(a) What is the probability of getting 4 or fewer correct guesses? Round your answer to 3 decimal places.

(b) Would 4 be an unusually low number of correct guesses? Use the criteria that a number (x) is unusually low if P(x or fewer) ≤ 0.05.
Yes, that is an unusually low number of correct guesses. No, that is not an unusually low number of correct guesses.

*Unusually low and high number of successes:
x successes among n trials is an unusually high number of successes if P(x or more) ≤ 0.05.
x successes among n trials is an unusually low number of successes if P(x or fewer) ≤ 0.05.

Calculate the following binomial probability by either using one of the binomial probability tables, software, or a calculator using the formula below. Round your answer to 3 decimal places.
P(x | n, p) =
n!/((n - x)! x!)
•px•q^{n - x} where q = 1 - p

P(x = 6, n = 7, p = 0.4) =